Answer
$\mathbf{r}(t)=(3\cos{t})\mathbf{i}+(t+\sin{t})\mathbf{j}$
Work Step by Step
In this problem, we are given $x=3\cos{t}$, and $y=t+\sin{t}$.
These can be directly substituted into the form $\mathbf{r}=x(t)\mathbf{i}+y(t)\mathbf{j}$ to arrive at this answer.
$\mathbf{r}(t)=(3\cos{t})\mathbf{i}+(t+\sin{t})\mathbf{j}$
